Multiple input, multiple output system and method

ABSTRACT

A linear transformation of parallel multiple input, multiple output (MIMO) encoded streams; also, space-time diversity and asymmetrical symbol mapping of parallel streams. Separately or together, these improve error rate performance as well as system throughput. Preferred embodiments include CDMA wireless systems with multiple antennas.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part from parent application Ser.Nos. 10/135,611 (TI-32969) and 10/135,679 (TI-32970), filed Apr. 30,2002 and claims priority from provisional application Ser. Nos.60/287,998, filed May 1, 2001 and 60/288,209, filed May 2, 2001.

BACKGROUND OF THE INVENTION

The present invention relates to wireless digital communications, andmore particularly to space-time diversity transmission systems andmethods.

Spread spectrum wireless communications utilize a radio frequencybandwidth greater than the minimum bandwidth required for thetransmitted data rate, but many users may simultaneously occupy thebandwidth. Each of the users has a pseudo-random code for “spreading”information to encode it and for “despreading” (by correlation) receivedspread spectrum signals and recovery of information. Such multipleaccess typically appears under the name of code division multiple access(CDMA). The pseudo-random code may be an orthogonal (Walsh) code, apseudo-noise (PN) code, a Gold code, or combinations (modulo-2additions) of such codes. After despreading the received signal at thecorrect time instant, the user recovers the corresponding informationwhile other users' interfering signals appear noise-like. For example,the interim standard IS-95 for such CDMA communications employs channelsof 1.25 MHz bandwidth and a pseudo-random code pulse (chip) intervalT_(c) of 0.8138 microsecond with a transmitted symbol (bit) lasting 64chips. The recent 3GPP wideband CDMA (WCDMA) proposal employs a 3.84 MHzbandwidth and the CDMA code length applied to each information symbolmay vary from 4 chips to 256 chips. Indeed, UMTS (universal mobiletelecommunications system) approach UTRA (UMTS terrestrial radio access)provides a spread spectrum cellular air interface with both FDD(frequency division duplex) and TDD (time division duplex) modes ofoperation. UTRA currently employs 10 ms duration frames partitioned into15 time slots with each time slot consisting of 2560 chips (T_(C)=0.26microsecond).

The air interface leads to multipath reception, so a RAKE receiver hasindividual demodulators (fingers) tracking separate paths and combinesthe finger results to improve signal-to-noise ratio (SNR). The combiningmay use a method such as the maximal ratio combining (MRC) in which theindividual detected signals in the fingers are synchronized and weightedaccording to their signal strengths or SNRs and summed to provide thedecoding. That is, a RAKE receiver typically has a number of DLL or TDLcode tracking loops together with control circuitry for assigningtracking units to the strongest received paths. Also, an antenna arraycould be used for directionality by phasing the combined signals fromthe antennas.

Further, UTRA allows for space-time block-coding-based transmit antennadiversity (STTD) in which, generically, channel bits b₀, b₁, b₂, b₃(values ±1) are transmitted as the sequence b₀, b₁, b₂, b₃ by antenna 1and simultaneously transmitted as the sequence −b₂, b₃, b₀, −b₁ byantenna 2. Note that interpreting (b₀, b₁) and (b₂, b₃) as two complexnumbers (e.g., QPSK or QAM symbols) implies the sequence transmitted byantenna 2 differs from the sequence from antenna 1 by a rotation of π/2in a two-complex-dimensional space followed by complex conjugation.

STTD is a diversity technique in the sense that it provides redundancyfor the transmitted symbols. Recently, efforts in standardization ofhigh speed downlink packet access (HSDPA) in WCDMA have taken place. Theuse of multiple antennas at the transmitter as well as the receiver isconsidered as a candidate technology. While STTD fits nicely in thegrand scheme, STTD does not provide any increase in data rate relativeto the current WCDMA systems.

Naguib et al, Increasing Data Rate over Wireless Channels, IEEE SignalProc. Mag. 76 (May 2000) considers multiple antennas for bothtransmitter and receiver together with synchronous cochannel space-timecoding (STTD) and interference cancellation. This approach can beadopted for HSDPA systems with 4 antennas at the base station, whereeach of the two pairs of antennas transmits one distinct data stream.This results in the transmission of two independent data streams, andthus doubles the system data rate as well as capacity. This scheme isthus double STTD (DSTTD) for a 4-antenna transmitter, or multiple STTDfor a 2n-antenna transmitter with n>2.

For high data rate systems, the performance of a scheme can be evaluatedbased on the error rate (bit error rate, symbol error rate, frame errorrate) as well as system throughput (the total data rate the system cansupport). While double/multiple STTD provides increased data rate andreasonably good performance, it can still be improved in somecircumstances.

For practical wireless communication systems employing multipleantennas, small inter-element spacing is desirable. However, this oftenresults in large correlation between the channel parameters especiallywhen the channel angular spread is small. For high data rate schemessuch as double/multiple STTD, high channel correlation results insignificant performance loss due to the loss in diversity gain as wellas decrease in the ability to separate multiple independent datastreams.

SUMMARY OF THE INVENTION

The present invention provides encoding/decoding with a channel adaptinglinear transform of parallel multiple input, multiple output streams.

This has the advantages including increased performance (in terms oferror rate and system throughput) for wireless communications.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are heuristic for clarity.

FIGS. 1 a-1 d are flow diagrams.

FIGS. 2 a-2 g illustrate preferred embodiment transmitter and receivers.

FIGS. 3-4 show other preferred embodiment transmitter and receiver.

FIGS. 5-9 present simulation results.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

1. Overview

FIGS. 1 a-1 d are flow diagrams for preferred embodiment transmissionand reception methods which include transmission using lineartransformations of parallel symbol streams with space-time transmitdiversity (STTD) encoding for multiple transmission antennas. Receptionresponds to the linear transformation. Alternative preferred embodimentdouble/multiple STTD encoding uses differing constellations fordiffering symbols streams with or without the linear transformation. Thelinear transformation adapts to the transmission channel conditions inorder to make the transformed channel matrix formally approximate thatof an independent identically distributed channel; this enhances channelcapacity and system performance by compensating for high correlation oftransmission channel coefficients as may arise from small spacing oftransmitter antennas. The linear transformation is updated to adapt tochanging channel conditions. Preferred embodiment approaches forsimplifying the linear transformation computation include restriction ofthe linear transformation to a permutation or quantization of itselements.

Preferred embodiment communications systems use preferred embodimentencoding and decoding methods, and FIGS. 2 a-2 c illustrate preferredembodiment transmitter and receiver functional blocks.

In preferred embodiment communications systems base stations and mobileusers could each include one or more digital signal processors (DSPs)and/or other programmable devices with stored programs for performanceof the signal processing of the preferred embodiment methods.Alternatively, specialized circuitry could be used. The base stationsand mobile users may also contain analog integrated circuits foramplification of inputs to or outputs from antennas and conversionbetween analog and digital; and these analog and processor circuits maybe integrated as a system on a chip (SoC). The stored programs may, forexample, be in ROM or flash EEPROM integrated with the processor orexternal. The antennas may be parts of receivers with multiple fingerRAKE detectors for each user's signals. Exemplary DSP cores could be inthe TMS320C6xxx or TMS320C5xxx families from Texas Instruments.

2. Four Transmit Antennas with one Receive Antenna Preferred Embodiments

FIG. 2 a illustrates a first preferred embodiment transmitter whichencodes two symbol streams (s₁ and S₂) with an STTD encoder for eachstream and transmits with four antennas, two antennas for each STTDencoder. This could be a base station transmitter in a cellular wirelesssystem. FIG. 2 b illustrates a preferred embodiment receiver with oneantenna for reception, such as for a mobile user in a cellular wirelesssystem. Preferred embodiments in subsequent sections include generalantenna arrangements. A base station may include the channel estimationand linear transformation computation as in FIG. 2 b.

The FIG. 2 a transmitter may operate according to the FIG. 1 a flow asfollows. Presume a block of data bits (with FEC) is channel encoded,block interleaved, and mapped to a block of symbols: . . . , s₁(n),s₂(n), s₁(n+1), s₂(n+1), s₁(n+2), s₂(n+2), s₁(n+3), s₂(n+3), . . . ,where each symbol s_(j)(k) is interpreted as a discrete complex number(e.g., QPSK, QAM, . . . ). The serial-to-parallel converter sends thestream . . . , s₁(n), s₁(n+1), s₁(n+2), s₁(n+3), . . . to the upper STTDencoder and the stream . . . , s₂(n), s₂(n+1), s₂(n+2), s₂(n+3), . . .to the lower STTD encoder. The upper STTD encoder has two outputsstreams: . . . , x₁(n), x₁(n+1), x₁(n+2), x₁(n+3), . . . , and . . . ,x₂(n), x₂(n+1), x₂(n+2), x₂(n+3), . . . , where pairwise the x_(j)( )sare equal to the s₁( )s: x₁(n)=s₁(n), x₁(n+1)=s₁(n+1) andx₂(n)=−s₁*(n+1), x₂(n+1)=s₁*(n). That is, the x₁ stream is just the s₁stream and the x₂ stream is the pairwise rotation intwo-complex-dimensional space of the s₁ stream. Analogously, the lowerSTTD encoder has two outputs streams: . . . x₃(n), x₃(n+1), x₃(n+2),x₃(n+3), . . . , and . . . , x₄(n), x₄(n+1), x₄(n+2), x₄(n+3), . . .where again pairwise the x_(j)( )s are equal to the s₂( )s: x₃(n)=s₂(n),x₃(n+1)=s₂(n+1) and x₄(n)=−s₂*(n+1), x₄(n+1)=s₂*(n).

The W block linearly transforms the four streams x₁(n), x₂(n), x₃(n),x₄(n) into the four streams y₁(n), y₂(n), y₃(n), y₄(n); that is, Wtransforms four symbol streams into four streams of linear combinationsof symbols. W adapts to transmission channel conditions as describedbelow; and the choice of W enhances channel capacity. Note that the flowof FIG. 1 a presumes that the transmitter also receives signals in thesame channel as its transmissions so that the transmitter can estimatethe physical channel coefficients and compute W; otherwise, thetransmitter must obtain W from the receiver to which it transmits. Forthe case of a CDMA system each of the four outputs y_(j)(n) is nextspread (multiplied by a common spreading code). Then the (spread)transformed-symbol streams drive modulators (pulse generators (at thechip rate) with essentially cosine and sine pulses for the real (inphase) and imaginary (quadrature) components of the (spread) y_(j)(n))which modulate the carrier wave radiated by the correspondingtransmitter antennas. For preferred embodiments not using CDMA, omit thespreading and operate the pulse generators at the symbol rate. For anOFDM (orthogonal frequency division multiplexing) system eachsub-carrier (tone) would have its own double/multiple STTD and lineartransformation.

FIG. 2 b illustrates a first preferred embodiment receiver with oneantenna which operates as indicated by FIG. 1 b. The antenna connects toa down-converter which drives a RAKE detector having one or moretracking fingers (including a sub-chip-rate sampler for A/D conversion,early-late chip synchronizer with despreading correlator, path channelestimation) to track resolvable received multipath signals, and themultipath detected signals may be combined using SNR weights. All fourtransmitter spreaders use the same spreading code; this increasescapacity in that other spreading codes may be used for other datastreams. Small spacing among the four transmitter antennas implies highcorrelation among the transmission channel coefficients in that eachpath from one transmitter antenna likely has corresponding highlycorrelated paths from the other three transmitter antennas. This alsoimplies near synchrony of the received symbols from the four transmitterantennas along four highly correlated paths and a single despreadercaptures all four paths in a receiver RAKE finger. Of course, thechannel coefficients for the four highly-correlated paths must differsomewhat in order to distinguish the s₁ and S₂ symbols; and the lineartransformation W effectively utilizes these differences. Preferredembodiment receivers with two or more antennas (see below) providefurther channel coefficient variety.

Denote the received (despread) baseband signal for symbol interval n asr(n)=h ₁ y ₁(n)+h ₂ y ₂(n)+h ₃ y ₃(n)+h ₄ y ₄(n)+w(n)where h_(m) is the baseband channel coefficient for the channel path(s)from the mth transmitter antenna to the receiver antenna and w(n) ischannel white noise. Note that the h_(m) vary with n, but this variationis slow and thus ignored (except for channel estimation updates) and notexplicit in the notation. Estimate the h_(m) by intermittentlytransmitting pilot symbols from each of the four transmitter antennas;FIG. 2 b indicates channel estimation.

First analyze the receiver in the simplest case of they_(m)(n)=x_(m)(n), which corresponds to the transformation matrix W=I₄(the 4×4 identity matrix). That is, consider:

$\begin{matrix}{{r(n)} = {{h_{1}{x_{1}(n)}} + {h_{2}{x_{2}(n)}} + {h_{3}{x_{3}(n)}} + {h_{4}{x_{4}(n)}} + {w(n)}}} \\{= {{h_{1}{s_{1}(n)}} + {h_{2}\left( {{- s_{1}}*\left( {n + 1} \right)} \right)} + {h_{3}{s_{2}(n)}} + {h_{4}\left( {{- s_{2}}*\left( {n + 1} \right)} \right)} + {w(n)}}}\end{matrix}$and so

$\begin{matrix}{{r^{*}\left( {n + 1} \right)} = {{h_{1}^{*}{x_{1}^{*}\left( {n + 1} \right)}} + {h_{2}^{*}{x_{2}(n)}} + {h_{3}^{*}{x_{3}^{*}\left( {n + 1} \right)}} + {h_{4}^{*}{x_{4}\left( {n + 1} \right)}} + {w^{*}\left( {n + 1} \right)}}} \\{= {{h_{1}^{*}{s_{1}^{*}\left( {n + 1} \right)}} + {h_{2}^{*}{s_{1}(n)}} + {h_{3}^{*}{s_{2}^{*}\left( {n + 1} \right)}} + {h_{4}^{*}{s_{2}(n)}} + {w^{*}\left( {n + 1} \right)}}}\end{matrix}$This can be expressed in terms of 2-vectors and 2×2 matrices as:r=A ₁ s ₁ +A ₂ s ₂ +wwhere r is the 2-vector of components r(n), r*(n+1); s₁ is the 2-vectorof components s₁(n), s₁*(n+1); s₂ is the 2-vector of components s₂(n),S₂*(n+1); A₁ is a 2×2 matrix corresponding to the channel path(s) of theupper pair of transmitter antennas in FIG. 2 a to the receiver antennawith the first row of A₁ equal h₁, −h₂ and second row h₂*, h₁*; A₂ is a2×2 matrix corresponding to the channel path(s) of the lower pair oftransmitter antennas to the receiver antenna with the first row h₃, −h₄and second row h₄*, h₃*; and w is a 2-vector with white noisecomponents.

The notation can be further compressed with the following definitions:4×1 vector s as the vertical concatenation of s₁ and S₂; and 2×4 matrixA as the horizontal concatenation of A₁ and A₂ (thus the first row of Ais [h₁, −h₂, h₃, −h₄] and the second row is [h₂*, h₁*, h₄*, h₃*]. Withthese definitions:r=A s+wThe matrix A is the 2×4 effective channel coefficient matrix of thechannel from the four transmitter antennas to the receiver antenna.

The two signals transmitted by the two transmitter antennas fed from thesame STTD encoder (e.g., x₁ and x₂ or x₃ and X₄) will not interfere witheach other due to the orthogonality provided by the STTD encoding.Indeed, at receiver antenna 1 the portion of the 2-vector [r(n), r(n+1)]from transmitter antenna 1 is [h₁s₁(n), h₁s₁(n+1)] and the portion fromtransmit antenna 2 is [−h₂s₁*(n+1), h₂s₁*(n)], and the complex innerproduct of these two vectors ish₁s₁(n){−h₂s₁*(n+1)}*+h₁s₁(n+1){h₂s₁*(n)}*=0. However, any combinationof two signals coming from different STTD encoders interfere with eachother and need to be separated using an interference resistant detector.Some examples of interference resistant detection scheme are the maximumlikelihood (which is optimal) detection, linear detection (zero forcingor minimum mean square error (MMSE)), and iterative detection (zeroforcing or MMSE). Both linear and iterative detectors are based on theidea of interference suppression and/or cancellation.

Since the matrix A is 2×4, linear and iterative detectors are notapplicable in this scenario. The maximum likelihood detector, however,can still be utilized. In general, a maximum likelihood detectionestimates the transmitted symbols s by ŝ which is the 4-vector ofsymbols that minimizes the sum of the error in the received signal onthe receiver antenna:min ∥r−Aŝ∥ ²=min ∥r−(A ₁ ŝ ₁ +A ₂ ŝ ₂)∥²Because there are a finite number of symbols in a constellation (e.g.,QAM, QPSK, . . . ), there are only a finite number of symbol pairs tosearch for the minimization. And the minimization computations can usethe channel estimates Â (derived from received known pilot symboltransmissions) in place of A. Further, the detector output may be a soft(log of symbol probability) output for each possible symbol; a MAPdecoder would use such detector outputs.

The computations (search over the finite set of possible ŝ) can berecast by left multiplication with A^(H) where ^(H) indicates Hermitianconjugate. This recasting provides a direct analysis below for thelinear transformation W. Thus set:z=A ^(H) r=A ^(H)(A s+w)=C s+A ^(H) wThen the decoding minimization formally becomesmin(z−Cŝ)^(H)C⁻¹(z−Cŝ)where C is the 4×4 Hermitian matrix A^(H) A which can be viewed as a 2×2array of 2×2 matrices A_(k) ^(H)A_(m) for k,m=1, 2 with

$\begin{matrix}{{A_{1}^{H}A_{1}} = {\left( {{h_{1}}^{2} + {h_{2}}^{2}} \right)I_{2}\mspace{14mu}\left( {I_{2}\mspace{14mu}{is}\mspace{14mu} 2 \times 2\mspace{14mu}{identity}\mspace{14mu}{matrix}} \right)}} \\{{A_{2}^{H}A_{2}} = {\left( {{h_{3}}^{2} + {h_{4}}^{2}} \right)I_{2}}} \\{{A_{1}^{H}A_{2}} = \begin{bmatrix}\left( {{h_{1}^{*}h_{3}} + {h_{2}h_{4}^{*}}} \right) & {- \left( {{h_{1}^{*}h_{4}} - {h_{2}h_{3}^{*}}} \right)} \\\left( {{h_{1}^{*}h_{4}} + {h_{2}h_{4}^{*}}} \right)^{*} & \left( {{h_{1}^{*}h_{3}} - {h_{2}h_{4}^{*}}} \right)^{*}\end{bmatrix}} \\{{A_{2}^{H}A_{2}} = \left( {A_{1}^{H}A_{2}} \right)^{H}}\end{matrix}$That is, C consists of STTD-encoded 2×2 subblocks and reflects thephysical channel which determines performance of the communicationsystem.

Now for W in general; choose W so that the corresponding transformed C,denoted {hacek over (C)}, will resemble the channel matrix of anindependent, identically distributed channel in that: (1) expectationsof off-diagonal elements are close to 0 and (2) expectations ofon-diagonal elements are uniform. The off-diagonal elements reflect theaverage additional interference due to channel correlations, and thesmallest on-diagonal element corresponds to the stream with the worstsignal to interference plus noise ratio (SINR) which dominatesperformance. Thus transform with W to approximate optimal channelperformance; so channel correlation underlies the choice of W asfollows.

Presume a Rayleigh fading channel so the h_(m) are normally distributedcomplex random variables with zero means. And the 4×4 channel covariancematrix, R, is the expectation of the 4×4 matrix of pairwise products ofchannel coefficients; that is, for k,m=1, 2, 3, 4:R_(k,m)=E[h_(k)h_(m)*]For fading channels with rich scatterers (typical conditions forcellular wireless), the scattering at the transmitter and at thereceiver are independent; and this independence, in general, implies Rdecomposes as the tensor product of the transmitter spatial covariancematrix R_(TX) (elements ρ_(TX)(k,m)) and the receiver spatial covariancematrix R_(RX) (elements ρ_(RX)(i,j)). That is, R=R_(RX)

R_(TX); or in other words, E[h_(ik)h_(jm)*]=ρ_(RX)(i,j) ρ_(TX)(k,m). Forthe preferred embodiments with 4 transmitter antennas and one receiverantenna:E[h_(k)h_(m)*]=ρ_(RX)(1,1)ρ_(TX)(k,m) for k,m=1, 2, 3, 4Thus ρ_(RX)(1,1) is just a multiplicative constant, and the relativevalues of the ρ_(TX)(k,m) determines the detection.

Estimate (e.g., maximum likelihood) the 4×4 transmitter covariancematrix, R_(TX), by a sample covariance matrix which can be obtained fromaveraging the channel coefficient estimates ĥ_(m) over multiple symbolintervals. Because R_(TX) is Hermitian, there are only 4 diagonal plus 6upper (or lower) triangular independent elements to estimate.ρ_(RX)(1,1)ρ_(TX)(k,m)=(1/N)Σ_(1≦n≦N) ĥ _(k) [n]ĥ _(m) *[n]where N is the number of samples and the ĥ_(m)[n] are the channelcoefficient estimates for symbol interval n. The number of samples Nused may depend upon the fading rate of the channel; but a heuristicrule of thumb takes N>5L where L is the length of vector h_(m). Theestimates ĥ_(m) (from a pilot channel) are available from the space-timecombining operation.

Now consider the effect of a linear transformation W. As illustrated inFIG. 2 a the y_(m)(n) are expressed in terms of the x_(m)(n) by thelinear transform W. Thus write x₁(n), x₂(n), x₃(n), x₄(n) as a 4-vectorx(n) and similarly write y₁(n), y₂(n), y₃(n), y₄(n) as the 4-vectory(n), and take y(n)=W*x(n) where W is a 4×4 complex matrix and W* is thecomplex conjugate of W. Thus the received signal r(n) can be expressedin terms of the x_(m) for general W by

$\begin{matrix}{{r(n)} = {{h_{1}{y_{1}(n)}} + {h_{2}{y_{2}(n)}} + {h_{3}{y_{3}(n)}} + {h_{4}{y_{4}(n)}} + {w(n)}}} \\{= {{\hslash_{1}{x_{1}(n)}} + {\hslash_{2}{x_{2}(n)}} + {\hslash_{3}{x_{3}(n)}} + {\hslash_{4}{x_{4}(n)}} + {w(n)}}}\end{matrix}$Take h to be the 4-vector with components h₁, h₂, h₃, h₄ and

the 4-vector components

₁,

₂,

₃,

₄, and thus

=W^(H) h. In other words, the transformed physical channel in terms of xhas channel coefficients

:

$\begin{matrix}{r = {\left\langle h \middle| y \right\rangle + w}} \\{= {\left\langle h \middle| {W^{*}x} \right\rangle + w}} \\{= {\left\langle {W^{H}h} \middle| x \right\rangle + w}} \\{= {\left\langle \hslash \middle| x \right\rangle + w}}\end{matrix}$Likewise in terms of x, the 2×2 STTD channel matrices are {hacek over(A)}₁ with first row [

₁, −

₂] and second row [

₂*,

₁*], and {hacek over (A)}₂ with first row [

₃, −

₄] and second row [

₄*,

₃*]; the channel matrix {hacek over (C)}={hacek over (A)}^(H){hacek over(A)}; the transmitter covariance {hacek over (R)}_(TX)=W^(H)R_(TX) W,and the covariance {hacek over (R)}=(I

W)^(H) R (I

W) where I is the 1×1 identity matrix from the receiver with oneantenna. (If the receiver has one antenna with a Q-finger RAKE detector,then this is essentially the same as Q separate antennas and thereceiver covariance matrix R_(RX) is Q×Q and will reflect the RAKEcombining; the following section considers multiple receiver antennas.)

The preferred embodiments choose W so the transformed channel matrix{hacek over (C)} approximates that of an independent, identicallydistributed channel. This translates into finding the W that minimizesthe expectation of the off-diagonal terms of {hacek over (C)} and thatuniformizes the expectations of the on-diagonal terms. First, presume anormalization: trace{W^(H)W}=4. Next, because only relative size amongthe

_(m) matters, normalize by taking trace{{hacek over (R)}_(TX)}=4; thisimplies E[|

₁|²+|

₂ ²+|

₃|²+|

₄|²]=4. Then find W to minimize the sum of off-diagonal terms ΣΣ_(k≠m)trace{E[{hacek over (A)}_(k) ^(H){hacek over (A)}_(m)]} and uniformizeon-diagonal terms so E[|

₁|²+|

₂|²]=E[|

₃|²+|

₄|²]=2. FIG. 1 b illustrates the foregoing flow, includingintermittently updating the channel coefficient estimation and resultantW computation. And FIG. 2 b shows a receiver block diagram.

More explicitly, a minimization of the off-diagonal elements togetherwith uniformization of the on-diagonal elements of E[{hacek over (C)}]is taking W tomin{|E[

₁*

₃+

₂

₄*]|²+|E[

₁*

₄−

₂

₃*]|²}min{|E[|

₁|²+|

₂|²]−2|}Thus the overall detection approach in FIG. 2 b starts with estimates ofthe physical channel coefficients, h_(m), as from pilot symbols, andthese estimates (after linear transformation with the then-current W)are used to make {hacek over (A)} for detection. Of course, the W usedfor detection at the receiver must match the W used by the transmitter.And, for a W update, the recent channel estimates are used to generateestimates of the correlation expectations E[h_(k)h_(m)*] which aretransformed by a W into the transformed channel correlation expectationsE[

_(k)

_(m)*] and also, by combinations, into elements of an updated E[{hacekover (C)}]. Hence, update W by picking the transformation which makesE[C] approximate the maximum capacity channel with 0 off-diagonalelements and uniform on-diagonal elements. Intermittently (periodically)perform this update computation of W to adapt to changing channelconditions. The channel coefficients estimation could be a movingaverages over a few slots (e.g., 3 slots, 6 slots, 15 slots with a 0.667msec slot in WCDMA); or the estimation could be at the symbol rate byrunning the pilot through a simple smoothing filter, especially for highfading rates conditions. The W update may be once a transmission timeinterval which may be 1 slot, 3 slots, 5 slots, 15 slots. Moreadaptively, the updates could be according to an analysis of currentchannel estimates.

After finding W, which may be performed by both the transmitter and thereceiver or just by the receiver and conveyed to the transmitter, thetransmitter applies W to transmissions as illustrated in FIGS. 1 a, 2 a.Similarly, the receiver applies W to its estimates of physical channelcoefficients

_(m) from pilot transmissions to recover the transformed physicalchannel coefficients

_(m) and then the STTD matrices {hacek over (A)}_(m) by expectations.The {hacek over (A)}_(m) are used for space-time decoding as shown inFIGS. 1 b, 2 b by finding ŝ to minimizemin({hacek over (A)}^(H)r−{hacek over (C)}ŝ)^(H){hacek over(C)}⁻¹({hacek over (A)}^(H)r−{hacek over (C)}ŝ)where. {hacek over (C)} is roughly the identity matrix. In this case,one may approximate the maximum likelihood matrix asmin ∥{hacek over (A)}^(H)r−{hacek over (C)}ŝ∥²

The minimization computations optimally consider all possible W and leadto complex computations. In the case of time-division duplexing (TDD)with base station transmission and reception (from mobiles) in the same(reciprocal) physical channel, the W computation may be performed at thebase station using its channel estimates as in FIG. 1 a; the basestation typically has available computational power. The W used at thetransmitter can be communicated to the receiver for detection.Alternatively, the receiver itself may also compute W based on its mostrecent or delayed channel estimates.

In contrast, for frequency-division duplexing (FDD) the W must becomputed at the mobile receiver (the base station receives signals fromthe mobile in a different frequency band) and communicated to the basestation via a feedback channel; consequently, quantization of W permitscomputations to be performed by searching (comparison-feedback) oversmaller sets of possible Ws. A one-shot approach compares all possiblechoices of W and then progressively signals the quantized elements of Wback to the transmitter, most significant bits first. Alternatively,partition the set of all possible W into subsets: S₁, S₂, . . . S_(K).Then at an update time t the receiver compares the choices of W in acorresponding subset S_(k(t)), and the resulting best (minimizing)choice W^((k)) from this subset is then compared to the then-currentprevious best choices W⁽¹⁾, . . . , W^((K)) from the other subsets, andthe best W^((t)) of these W⁽¹⁾, . . . , W^((k)), . . . , W^((K)) is usedas the update and sent to the transmitter.

Another low complexity approach restricts W to be a permutation of thex_(m); that is, y₁(n)=x_(π(1))(n), y₂(n)=x_(π(2))(n), y₃(n)=x_(π(3))(n),y₄(n)=x_(π(4))(n) where π is a permutation of {1,2,3,4}. Thus W will bea matrix with 4 elements equal to 1 and the remaining 12 elements equalto 0; and

_(π(m))=h_(m). For an FDD system, the restriction to a search of onlypermutation Ws reduces the computation complexity for a mobile receiverwhich may have limited computational power. This is also particularlybeneficial when the feedback resource is limited and/or the channelchanges at a faster rate. By symmetry not all permutations must beconsidered; for example, interchanging s₁ and s₂ has no effect on thechannel. Indeed, there are only 6 different permutations. Note that withW a permutation, the minimization constraint trace{W^(H)W}=4automatically occurs, and the constraint E[|

₁|²+|

₂|²]=E[|

₃|²+|

₄|²]=2 translates to choosing from three possibilities (permutations):(1) E[|h₁|²+|h₂|²]≅E[|h₃|²+|h₄|²]≅2; (2)E[|h₁|²+|h₃|²]≅E[|h₂|²+|h₄|²]≅2; or (3) E[|h₁|²+|h₄|²]≅E[|h₂|²+|h₃|²]≅2.

When the power across all the channel coefficients is uniformlydistributed (that is, E[|h_(p)|²]=1 for all p), the above constraintsare automatically satisfied. In this case, it suffices to consider onlythe minimization of the off-diagonal terms of E[{hacek over (C)}].Otherwise, a tradeoff between the off-diagonal minimization andon-diagonal uniformization can be used. For example, the permutationmatrix W may be chosen as the minimization:min{v₁|E[h_(π(1))*h_(π(3))+h_(π(2))h_(π(4))*]|²+v₂|E[h_(π(1))*h_(π(4))−h_(π(2)h)_(π(3))*]|²+v₃|E[|h_(π(1))|²+|h_(π(2))|²]−2|²}where v₁, v₂, and v₃ are weighting parameters that are chosen to achievethe desired degree of trade-off.

Further, the approach of restricting W to be a permutation can beexpanded to include weighting of the nonzero elements of W. Inparticular, with permutation π, take y₁(n)=w_(π(1))x_(π(1))(n),y₂(n)=w_(π(2))x_(π(2))(n), y₃(n)=W_(π(3))x_(π(3))(n),y₄(n)=w_(π(4))x_(π(4))(n) where the set of weights {w₁, w₂, w₃, w₄} arenonzero and may be quantized to further limit complexity. In this casethe constraint trace{W^(H)W}=4 translates into|w₁|²+|w₂|²+|w₃|²+|w₄|²=4.

3. Four Transmit Antennas with Multiple Receive Antennas PreferredEmbodiments

FIG. 2 c illustrates a first preferred embodiment receiver with Q (≧2)antennas and which, analogous to the one antenna receiver of FIG. 2 b,receives transmissions from the transmitter of FIG. 2 a; FIG. 1 c is aflow diagram. As FIG. 2 e illustrates a single antenna together with QRAKE fingers for tracking Q resolvable received paths can effectivelyoperate the same as Q antennas because Q resolvable paths will havediffering transmission channel coefficients. Similarly, othercombinations of antennas and fingers can be interpreted as multipleantennas with single fingers or a single antenna with multiple fingers.

Denote the received despread baseband signal for symbol interval n forreceiver antenna q (1≦q≦Q) asr _(q)(n)=h _(q1) y ₁(n)+h _(q2)y₂(n)+h _(q3) y ₃(n)+h _(q4) y ₄(n)+w_(q)(n)where h_(qm) is the baseband channel coefficient for the channel fromthe m^(th) transmitter antenna to receiver antenna q and w_(q)(n) ischannel white noise. Pilot symbols from each of the four transmitterantennas provide updating estimates for the h_(qm) as shown in FIG. 2 d.

FIG. 1 c is a flow diagram for the operation of the Q-antenna receiverwhich is analogous to and an extension of the operation of thepreviously-described one antenna receiver of FIG. 1 b. In particular,using notation analogous to that of the foregoing, take W* as the 4×4matrix that transforms x to y as before; then take h_(q) to be the4-vector with coefficients h_(q1), h_(q2), h_(q3), h_(q4), and set

_(q)=W^(H)h_(q), thus with a real inner product:

$\begin{matrix}{r_{q} = {\left\langle h_{q} \middle| y \right\rangle + w_{q}}} \\{= {\left\langle h_{q} \middle| {W^{*}x} \right\rangle + w_{q}}} \\{= {\left\langle {W^{H}h_{q}} \middle| x \right\rangle + w_{q}}} \\{= {\left\langle \hslash_{q} \middle| x \right\rangle + w_{q}}}\end{matrix}$or more explicitly,

$\begin{matrix}{{r_{q}(n)} = {{\hslash_{q\; 1}{x_{1}(n)}} + {\hslash_{q\; 2}{x_{2}(n)}} + {\hslash_{q\; 3}{x_{3}(n)}} + {\hslash_{q\; 4}{x_{4}(n)}} + {w_{q}(n)}}} \\{= {{\hslash_{q\; 1}{s_{1}(n)}} + {\hslash_{q\; 2}\left( {- {s_{1}^{*}\left( {n + 1} \right)}} \right)} + {\hslash_{q\; 3}{s_{2}(n)}} + {\hslash_{q\; 4}\left( {- {s_{2}^{*}\left( {n + 1} \right)}} \right)} + {w_{q}(n)}}}\end{matrix}$and

$\begin{matrix}{{r_{q}^{*}\left( {n + 1} \right)} = {{\hslash_{q\; 1}^{*}{x_{1}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 2}^{*}{x_{2}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 3}^{*}{x_{3}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 4}^{*}{x_{4}^{*}\left( {n + 1} \right)}} + {w_{q}^{*}\left( {n + 1} \right)}}} \\{= {{\hslash_{q\; 1}^{*}{s_{1}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 2}^{*}{s_{1}(n)}} + {\hslash_{q\; 3}^{*}{s_{2}\left( {n + 1} \right)}} + {\hslash_{q\; 4}^{*}{s_{2}(n)}} + {w_{q}^{*}\left( {n + 1} \right)}}}\end{matrix}$This can again be expressed in terms of 2-vectors and 2×2 matrices as:r _(q) ={hacek over (A)} _(q1) s ₁ +{hacek over (A)} _(q2) s ₂ +w _(q)where r_(q) is the 2-vector of components r_(q)(n), r_(q)*(n+1); s₁ isthe 2-vector of components s₁(n), s₁*(n+1); s₂ is the 2-vector ofcomponents s₂(n), s₂*(n+1); {hacek over (A)}_(q1) is a 2×2 matrixcorresponding to the channels of the upper pair x₁, x₂ in FIG. 1 a toreceiver antenna q with first row of {hacek over (A)}_(q1) equal

_(q1), −

_(q2) and second row

_(q2)*,

_(q1)*; {hacek over (A)}_(q2) is a 2×2 matrix corresponding to thechannels of the lower pair x₃, x₄ to receiver antenna q with first row

_(q3), −

_(q4) and second row

_(q4)*,

_(q3)*; and W_(q) is a 2-vector with white noise components.

As with the prior preferred embodiment, the notation can be furthercompressed with the following definitions: the 2Q×1 vector r with itsfirst two components equal the two components of r₁, next two componentsequal the two components of r₂, and so forth to the Qth last twocomponents equal to the two components of r_(Q) (i.e., verticalconcatenation of r₁, r₂, . . . , r_(Q)), 4×1 vector s as the verticalconcatenation of s₁ and s₂; and 2Q×4 matrix {hacek over (A)} as the Q×2array of 2×2 matrices {hacek over (A)}₁₁ {hacek over (A)}₁₂; {hacek over(A)}₂₁ {hacek over (A)}₂₂; . . . {hacek over (A)}_(Q1) {hacek over(A)}_(Q2) (thus the first row of {hacek over (A)} is [

₁₁, −h₁₂, h₁₃, −h₁₄] and second row [h₁₂*, h₁₁*, h₁₄*, h₁₃*], third row[h₂₁, −h₂₂, h₂₃, −h₂₄], fourth row [h₂₂*, h₂₁*, h₂₄*, h₂₃*], and soforth down to the 2Qth row [h_(Q2)*, h_(Q1)*, h_(Q4)*, h_(Q3)*]. Withthis notation:r={hacek over (A)}s+wThe matrix {hacek over (A)} is the 2Q×4 effective transformed channelcoefficient matrix of the 4Q paths: one from each of the four x_(m) toeach of the Q receiver antennas. The 4×4 transformation matrix W will bedetermined as previously by approximating an independent, identicallydistributed channel.

As with the previous preferred embodiments, form {hacek over (C)} as the4×4 Hermitian TI-32969AA Page 17 matrix {hacek over (A)}^(H){hacek over(A)} which can be viewed as a 2×2 array of sums of 2×2 matrices {hacekover (A)}_(q,k) ^(H){hacek over (A)}_(q,m) with the sums over q in therange 1≦q≦Q for each k,m=1, 2, where{hacek over (A)} _(q1) ^(H) {hacek over (A)} _(q1)=(|h _(q1)|² +|h_(q2|) ²)I ₂ (I₂ is 2×2 identity matrix){hacek over (A)} _(q2) ^(H) {hacek over (A)} _(q2)=(|h _(q3)|² +|h_(q4)|²)I ₂

${{\overset{\Cup}{A}}_{q\; 1}^{H}{\overset{\Cup}{A}}_{q\; 2}} = \begin{bmatrix}\left( {{h_{q\; 1}^{*}h_{q\; 3}} + {h_{q\; 2}h_{q\; 4}^{*}}} \right) & {- \left( {{h_{q\; 1}^{*}h_{q\; 4}} - {h_{q\; 2}h_{q\; 3}^{*}}} \right)} \\\left( {{h_{q\; 1}^{*}h_{q\; 4}} - {h_{q\; 2}h_{q\; 3}^{*}}} \right)^{*} & \left( {{h_{q\; 1}^{*}h_{q\; 3}} + {h_{q\; 2}h_{q\; 4}^{*}}} \right)\end{bmatrix}${hacek over (A)}_(q2) ^(H){hacek over (A)}_(q1)=({hacek over (A)}_(q1)^(H){hacek over (A)}_(q2))^(H)

That is, {hacek over (C)} consists of sums of STTD-encoded 2×2 subblocksand reflects the transformed physical channel which determinesperformance of the communication system. Again, the preferredembodiments choose the transformation W to enhance capacity of thephysical channel C to yield the transformed physical channel {hacek over(C)}.

As with the preceding preferred embodiments, the covariance matrix Rdecomposes as the tensor product of the transmitter spatial covariancematrix R_(TX) (elements ρ_(TX)(k,m)) and the receiver spatial covariancematrix R_(RX) (elements ρ_(RX)(i,j)). That is, R=R_(RX)

R_(TX); or for the preferred embodiments with 4 transmitter antennas andQ receiver antennas:

E[h_(qp)h_(q′p′)*]=ρ_(RX)(q,q′) ρ_(TX)(p,p′) for p,p′=1, . . . , 4;q,q′=1, . . . , Q But then for each pair q,q′, all of the ρ_(TX)(p,p′)can be found up to the multiplicative constant ρ_(RX)(q,q′). That is,the separability of the receiver covariance and transmitter covarianceimplies the previously analyzed case Q=1 suffices. And thetransformation W in general leads to the transformed transmittercovariance {hacek over (R)}_(TX)=W^(H R) _(TX) W and the transformedcovariance {hacek over (R)}=(I_(Q)

W)^(H) R (I_(Q)

W) where I_(Q) is the Q×Q identity matrix.

So repeat the previous: estimate the 4×4 transmitter covariance matrix,R_(TX), by a sample covariance matrix which can be obtained fromaveraging the channel state estimates ĥ_(qp) Lover multiple symbolintervals for one antenna qρ_(RX)(q,q)ρ_(TX)(p,p′)=(1/N)Σ_(1≦n≦N) ĥ _(qp) [n]ĥ _(qp′) *[n]where N is the number of samples in the average. The estimates ĥ (from apilot channel) are available from the space-time RAKE operation.Further, the estimates of ρ_(TX)(p,p′) from various receiver antennas qcan be averaged (with weightings) to improve the estimates.

Then find 4×4 W using any of the previous minimization approaches. The Qantennas implies the elements of 4×4 E[{hacek over (C)}] are sums overq. More explicitly, a minimization of the off-diagonal elements togetherwith uniformization of the on-diagonal elements of E[{hacek over (C)}]to find W becomes:min{|Σ_(1≦q≦Q)E[

_(q1)*

_(q3)+

_(q2)

_(q4)*]|²+|Σ_(1≦q≦Q)E[

_(q1)*

_(q4)−

_(q2)

_(q3)*]|²}min{|Σ_(1≦q≦Q)E[|

_(q1)|²+|

_(q2)|²]−2|²}with a normalization of Σ_(1≦q≦Q) E[|

_(q1)|²+|

_(q2)|²+|

_(q3)|²+|

_(q4)|²]=4.

Analogous to the Q=1 scenario, an interference resistant detector mustbe used to separate the two independent data streams from two STTDencoders. In general, the optimal maximum likelihood detection wouldestimate the transmitted symbols s by ŝ which is the vector of symbolsthat minimizes the sum of the errors in the received signal on thereceiver antennas:∥r₁−({hacek over (A)}₁₁ŝ₁+{hacek over (A)}₁₂ŝ₂)∥²+∥r₂−({hacek over(A)}₂₁ŝ₁+{hacek over (A)}₂₂ŝ₂)∥+ . . . +∥r_(Q)−({hacek over(A)}_(Q1)ŝ₁+{hacek over (A)}_(Q2)ŝ₂)∥²Such a maximum likelihood detection becomes computationally intensivewith larger antenna systems. Since the size of matrix {hacek over (A)}is 2Q×4, linear (1-shot) and iterative detectors with lower complexityare applicable when Q is at least 2. As mentioned before, both linearand iterative detectors are based on the idea of interferencesuppression/cancellation. Possible methods include zero forcing andminimum mean square error (MMSE). In the following, the linear MMSE(LMMSE) and iterative MMSE (IMMSE) detectors are explained. Azero-forcing-based detector can be obtained from its MMSE analog byremoving the second term in the matrix inverse.

Starting from the statistics z which is the output of the space-timeRAKE combiner (e.g., FIG. 2 d):z={hacek over (A)} ^(H) r={hacek over (A)} ^(H)({hacek over(A)}s+w)={hacek over (C)}s+{hacek over (A)}wthe LMMSE detector essentially performs a linear transformation F to thestatistics z such that the mean square error (MSE) E[∥F z−s∥²] isminimized. The (theoretically derived) linear transformation F is:F=({hacek over (C)}+N ₀ /E _(s) I ₄)⁻¹where N₀ is the energy of each of the 2Q components of the white noisew, E_(s) is the average energy of each symbol in s (assume that all thesymbols in s are of the same constellation, modulation scheme), and I₄is the 4×4 identity matrix. As noted above, the linear transformationfor linear zero-forcing (LZF) detector is simplyF=({hacek over (C)})⁻¹And the resulting minimum MSE for all of the 4 symbols in s correspondsto the diagonal elements of the matrix N₀F. The resulting linearlytransformed statistics y=Fz is essentially the soft estimate of s. Eachelement of y is then passed separately to a decision device (symboldetector) to provide the corresponding hard symbol estimate.

For systems with 4 transmit antennas, the iterative MMSE (IMMSE)detector is a sequence of 4 linear MMSE detection stages, where eachdetection provides the soft and hard symbol estimates for each of the 4symbols in s. In each of the 4 stages, a linear MMSE transformation isperformed. After the transformation, one symbol is selected fordetection (based on the post detection SINR). The signal correspondingto that symbol is then regenerated and subtracted from the receivedsignal. Let a₁, a₂, a₃, and a₄ denote the first, second, third, andfourth columns of matrix {hacek over (A)}. Also, let v(n) denote then-th element of a vector v. The following pseudo-code describes how anIMMSE detector operates:

B = [ a₁ a₂ a₃ a₄ ] for p=1 to 4 F = ( B^(H) B + N₀/E_(s) I)⁻  : (4−p+1)× (4−p+1) matrix y = F B^(H) r       : (4−p+1) ×1 vector Find thesmallest diagonal element of matrix F Select one out of (4−p+1) symbolsto be detected which corresponds to the smallest diagonal element ofmatrix F: let that be s(o(p) ) Obtain soft estimate of symbol s(o(p) )from the corresponding element of y Find the hard estimate of s(o(p) ):σ(o(p) ) r = r − a_(o(p)) σ (o(p) ) Remove column a_(o(p)) from B endNote that the symbol selection is based on the diagonal elements ofmatrix F, which correspond to symbol MSEs. Theoretically, the symbol MSEis inversely proportional to SINR.4. Multiple Antenna Preferred Embodiments

FIG. 2 c generalizes the foregoing transmitter from four transmitantennas to P antennas with P/2 separate STTD encoders for P/2 symbolstreams s₁, s₂, . . . , s_(P/2). The preceding preferred embodiments aremodified so that

$\begin{matrix}{{r_{q}(n)} = {{h_{q\; 1}{y_{1}(n)}} + {h_{q\; 2}{y_{2}(n)}} + \ldots + {h_{qP}{y_{P}(n)}} + {w_{q}(n)}}} \\{= {{\hslash_{q\; 1}{x_{1}(n)}} + {\hslash_{q\; 2}{x_{2}(n)}} + \ldots + {\hslash_{qP}{x_{P}(n)}} + {w_{q}(n)}}} \\{= {{\hslash_{q\; 1}{s_{1}(n)}} + {\hslash_{q\; 2}\left( {- {s_{1}^{*}\left( {n + 1} \right)}} \right)} + \ldots + {\hslash_{qP}\left( {- {s_{P/2}^{*}\left( {n + 1} \right)}} \right)} + {w_{q}(n)}}}\end{matrix}$and similarly

$\begin{matrix}{{r_{q}^{*}\left( {n + 1} \right)} = {{\hslash_{q\; 1}^{*}{x_{1}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 2}^{*}{x_{2}^{*}\left( {n + 1} \right)}} + \ldots + {\hslash_{qP}^{*}{x_{P}^{*}\left( {n + 1} \right)}} + {w_{q}^{*}\left( {n + 1} \right)}}} \\{= {{\hslash_{q\; 1}^{*}{s_{1}^{*}\left( {n + 1} \right)}} + {\hslash_{q\; 2}^{*}{s_{1}(n)}} + \ldots + {\hslash_{qP}^{*}{s_{P/2}(n)}} + {w_{q}^{*}\left( {n + 1} \right)}}}\end{matrix}$where W is a P×P linear transformation of P-vector x to P-vector y=W*xas in FIG. 2 d and

_(q)=W^(H)h_(q).

This can again be expressed in terms of 2-vectors and 2×2 matrices as:r _(q) ={hacek over (A)} _(q1) s ₁ +{hacek over (A)} _(q2) s ₂ + . . .+{hacek over (A)} _(qP/2) s _(P/2) +W _(q)where r_(q) is the 2-vector of components r_(q)(n), r_(q)*(n+1); s₁ isthe 2-vector of components s₁(n), s₁*(n+1); . . . , s_(P/2) is the2-vector of components s_(P/2)(n), s_(P/2)*(n+1); {hacek over (A)}_(q1)is a 2×2 matrix corresponding to the channels of the upper pair x₁, x₂in FIG. 2 d to receiver antenna q with first row of {hacek over(A)}_(q1) equal

_(q1), −

_(q2) and second row

_(q2)*,

_(q1)*; . . . , and {hacek over (A)}_(qP/2) is a 2×2 matrixcorresponding to the channels of the bottom pair x_(P-1), x_(P) toantenna q with first row

_(q,P-1), −

_(qP) and second row

_(qP)*,

_(q,P-1)*.

As with the prior preferred embodiment, the notation can be furthercompressed with the following definitions: the 2Q×1 vector r with itsfirst two components equal the two components of r₁, next two componentsequal the two components of r₂, and so forth to the Qth last twocomponents equal to the two components of r_(Q) (i.e., verticalconcatenation of r₁, r₂, . . . , r_(Q)), P×1 vector s as the verticalconcatenation of s₁, . . . s_(P/2); and 2Q×P matrix {hacek over (A)} asthe Q×P/2 array of 2×2 matrices {hacek over (A)}₁₁ {hacek over (A)}₁₂ .. . {hacek over (A)}_(1,P/2); {hacek over (A)}₂₁ {hacek over (A)}₂₂, . .. , {hacek over (A)}_(1,P/2); . . . {hacek over (A)}_(Q1) {hacek over(A)}_(Q2), . . . , {hacek over (A)}Q,P/2 (thus the first row of {hacekover (A)} is [

₁₁, −

₁₂,

₁₃, −

₁₄, . . . ,

_(1,P-1), −

_(1P)] and second row [

₁₂*,

₁₁*,

₁₄*,

₁₃*, . . . ,

_(1P)*,

_(1,P-1)*], third row [

₂₁, −

₂₂,

₂₃, −

₂₄, . . . ,

_(2,P-1), −

_(2P)], fourth row [

₂₂*,

₂₁*,

₂₄*,

₂₃*, . . . ,

_(2P)*,

_(2P-1)*], and so forth down to the 2Qth row [

_(Q2)*,

_(Q1)*,

_(Q4)*,

_(Q3)*, . . . ,

_(QP)*,

_(Q,P-1)*]. With this notation:r={hacek over (A)}s+wThe matrix A is the 2Q×P effective transformed channel coefficientmatrix of the PQ paths: one from each of the P transmitter antennas toeach of the Q receiver antennas. The P×P transformation matrix W will bedetermined as previously by approximating an independent, identicallydistributed channel.

Form {hacek over (C)} as the P×P Hermitian matrix {hacek over(A)}^(H){hacek over (A)} and which is a P/2×P/2 array of sums of 2×2STTD matrices {hacek over (A)}_(q,k) ^(H){hacek over (A)}_(q,m) with thesums over q in the range 1≦q≦Q for each k,m=1, 2, . . . P/2 where:

$\begin{matrix}\begin{matrix}{{{\overset{\Cup}{A}}_{qm}^{H}{\overset{\Cup}{A}}_{qm}} = {\left( {{\hslash_{q,{{2m} - 1}}}^{2} + {\hslash_{q,{2m}}}^{2}} \right)I_{2}}} & \; & \left( {I_{2}\mspace{14mu}{is}\mspace{14mu} 2 \times 2\mspace{14mu}{identity}\mspace{14mu}{matrix}} \right)\end{matrix} \\{{{\overset{\Cup}{A}}_{qk}^{H}{\overset{\Cup}{A}}_{qm}} = \begin{bmatrix}\left( {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{{2m} - 1}}} + {\hslash_{q,{2k}}\hslash_{q,{2m}}^{*}}} \right) & {- \left( {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{2m}}} - {\hslash_{q,{2k}}\hslash_{q,{{2m} - 1}}^{*}}} \right)} \\\left( {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{2m}}} - {\hslash_{q,{2k}}\hslash_{q,{{2m} - 1}}^{*}}} \right)^{*} & \left( {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{{2m} - 1}}} + {\hslash_{q,{2k}}\hslash_{q,{2m}}^{*}}} \right)^{*}\end{bmatrix}} \\{{{\overset{\Cup}{A}}_{qm}^{H}{\overset{\Cup}{A}}_{qk}} = \left( {{\overset{\Cup}{A}}_{qk}^{H}{\overset{\Cup}{A}}_{qm}} \right)^{H}}\end{matrix}$That is, {hacek over (C)} consists of sums of STTD-encoded 2×2 subblocksand reflects the transformed physical channel and determines performanceof the communication system. Again, the preferred embodiments choose thetransformation W to enhance capacity of the physical channel C to yieldthe transformed physical channel {hacek over (C)}.

As with the preceding preferred embodiments, the covariance matrix Rdecomposes as the tensor product of the transmitter spatial covariancematrix R_(TX) (elements ρ_(TX)(k,m)) and the receiver spatial covariancematrix R_(RX) (elements ρ_(RX)(i,j)). That is, R=R_(RX)

R_(TX); or for the preferred embodiments with P transmitter antennas andQ receiver antennas:E[h_(qp)h_(q′p′)*]=ρ_(RX)(q,q′)ρ_(TX)(p,p′) for p,p′=1, . . . , P;q,q′=1, . . . , QThen for each pair q,q′, all of the ρ_(TX)(p,p′) can be found up to themultiplicative constant ρ_(RX)(q,q′). That is, the separability of thereceiver covariance and transmitter covariance means that thepreviously-analyzed case Q=1 suffices. Indeed, the transformation W ingeneral leads to the transmitter covariance {hacek over (R)}_(TX)=W^(H)R_(TX) W and the covariance {hacek over (R)}=(I_(Q)

W)^(H) R (I_(Q)

W) where I_(Q) is the Q×Q identity matrix.

So repeating the previous: estimate the P×P transmitter covariancematrix, R_(TX), by a sample covariance matrix which can be obtained fromaveraging the channel state estimates ĥ_(qp) over multiple symbolintervals for one antenna qρ_(RX)(q,q)ρ_(TX)(p,p′)=(1/N)Σ_(1≦n≦N) ĥ _(qp) [n]ĥ _(qp′) *[n]where N is the number of samples in the average. The estimates ĥ (from apilot channel) are available from the space-time RAKE operation.

Then find W using any of the previous minimization approaches. Moreexplicitly, a minimization of the off-diagonal elements together withuniformization of the on-diagonal elements of E[{hacek over (C)}]implies picking W to achieve:

$\begin{matrix}{\min\left\{ {{{\sum\limits_{1 \leq q \leq Q}{E\left\lbrack {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{{2m} - 1}}} + {\hslash_{q,{2k}}\hslash_{q,{2m}}^{*}}} \right\rbrack}}} +} \right.} \\\left. {{\sum\limits_{1 \leq q \leq Q}{E\left\lbrack {{\hslash_{q,{{2k} - 1}}^{*}\hslash_{q,{2m}}} - {\hslash_{q,{2k}}\hslash_{q,{{2m} - 1}}^{*}}} \right\rbrack}}} \right\}\end{matrix}$$\min\left\{ {{{\sum\limits_{1 \leq q \leq Q}{E\left\lbrack {{\hslash_{q,{{2k} - 1}}}^{2} + {\hslash_{q,{2k}}}^{2}} \right\rbrack}} - 2}} \right\}$with a normalization of E[|

_(q1)|²+|

_(q2)|²+ . . . +|

_(qP)|²]=P and trace{W^(H)W}=P.

The same detection schemes (maximum likelihood, linear, and iterative)can be extended for an arbitrary value of P (even). When Q is at leastP/2, linear and iterative detection can be applied.

5. Extension for Multipath (Frequency Selective) Channels

When the channel is frequency selective (contains multiple propagationpaths with different delays), two possible scenarios can occur. Thefirst scenario is relevant to CDMA systems with large spreading gain(e.g. ≧128) and the channel delay spread is small compared to one symbolduration. In this case, different paths arriving at the receiver atdifferent delays can be resolved to provide multipath diversity withoutcausing significant amount of inter-symbol interference. Additional pathdiversity can be treated as having additional receive antennas (e.g.having 2-path diversity at each antenna is equivalent to having 2Qreceive antennas).

The second scenario is relevant to higher data rate systems where thechannel delay spread is sufficiently large compared to one symbolduration that the effect of inter-symbol interference is significant. Inthis case, multipath interference suppression can be used in conjunctionto the spatial interference resistant detector, especially when thenumber of users/codes is large and/or higher order modulation is used.The concept described above for selecting the best linear transformationW can be extended to this scenario.

6. MIMO Preferred Embodiment

The above description applies to systems that employ multiple STTDencoding. The aforementioned weighting technique for combating theeffect of correlated channels can also be applied to multi-inputmulti-output (MIMO) systems that do not employ any space-time coding. Asillustrated in the transmitter and receiver of FIGS. 2 f-2 g, denote thenumber of transmit and receive antennas as P and Q, respectively. Thereceived (despread) baseband signal across all receive antennas at anytime interval can be written in a Q-dimensional vector as:

$\begin{matrix}{r = {{h_{1}x_{1}} + {h_{2}x_{2}} + \ldots + {h_{P}x_{P}} + w}} \\{= {{\begin{bmatrix}h_{1} & h_{2} & \ldots & h_{P}\end{bmatrix}\begin{bmatrix}x_{1} & x_{2} & \ldots & x_{P}\end{bmatrix}}^{T} + w}} \\{= {{Hx} + w}}\end{matrix}$where h_(p) denotes the Q-vector channel corresponding to the p-thtransmit antenna, and x_(p) is the transmitted signal via the p-thtransmit antenna. The matrix H is the Q×P MIMO channel matrix and thevector x is the P×1 transmitted signal vector. Note that in this case,the time index (n) can be suppressed since the transmitted symbols areindependent across time.

Analogous to the weighting in multiple STTD encoded systems, the P×1transmitted signal vector x is obtained from the linearly transformedP×1 transmitted data symbol vector s. Denoting the P×P lineartransformation as W, we have x=Ws. Hence, r can be written asr=H W s+wUnlike in multiple STTD encoded systems, H contains the actual physicalchannel coefficients. That is, the (q,p)-th element of matrix Hcorresponds to the channel between the p-th transmit antenna and q-threceive antenna.

As with the preceding preferred embodiments, the covariance matrix R(where R_(k,m)=E[h_(k)h_(m)*]) decomposes as the tensor product of thetransmitter spatial covariance matrix R_(TX) (elements ρ_(TX)(k,m)) andthe receiver spatial covariance matrix R_(RX) (elements ρ_(RX)(i,j)).That is, R=R_(RX)

R_(TX); or for the preferred embodiments with P transmitter antennas andQ receiver antennas:E[h_(qp)h_(q′p′)*]=ρ_(RX)(q,q′)ρ_(TX)(p,p′) for p,p′=1, . . . , P;q,q′=1, . . . , QThen for each pair q,q′, all of the ρ_(TX)(p,p′) can be found up to themultiplicative constant ρ_(RX)(q,q′). That is, the separability of thereceiver covariance and transmitter covariance means that thepreviously-analyzed case Q=1 suffices.

Similar to that for multiple STTD, the P×P effective channel matrixafter maximum ratio combining (denoted M) isM=W^(H)H^(H)H Wwhere the (i,j)-th element of matrix H^(H)H is h_(i) ^(H)h_(j)=Σ_(1≦q≦Q)h_(iq)*h_(qj). Hence, the elements of matrix E[H^(H) H] can be directlyrelated to the elements of matrix R since Σ_(1≦q≦Q)E[h_(iq)*h_(qj)]=Σ_(1≦q≦Q)ρ_(RX)(i,q) ρ_(TX)(q,j).

The rule for choosing W is similar to that for multiple STTD systemsdescribed above: choose W so that the corresponding transformedE[H^(H)H], denoted E[M], will resemble the channel matrix of anindependent, identically distributed channel in that: (1) expectationsof off-diagonal elements are close to 0 and (2) expectations ofon-diagonal elements are uniform. The off-diagonal elements reflect theaverage additional interference due to channel correlations, and thesmallest on-diagonal element corresponds to the stream with the worstsignal to interference plus noise ratio (SINR), which dominatesperformance.

W is found using any of the previous minimization approaches. Moreexplicitly, let the (i,j)-th element of matrix E[M] be denoted asM_(ij). Then, the minimization of the off-diagonal elements togetherwith uniformization of the on-diagonal elements of E[M] implies pickingW to achieve:min{Σ_(1≦i≦P)Σ_(i≦j≦P)|M_(ij)|}min{Σ_(1≦i≦P)|M_(ij)−1 |}with a normalization of Σ_(1≦i≦P) M₁₁=P and trace{W^(H)W}=P.

The same detection schemes (maximum likelihood, linear, and iterative)can be extended for an arbitrary value of P. When Q is at least P,linear and iterative detection can be applied.

The minimization computations optimally consider all possible W and leadto complex computations. In the case of time-division duplexing (TDD)with base station transmission and reception (from mobiles) in the same(reciprocal) physical channel, the W computation may be performed at thebase station using its channel estimates as in FIG. 1 a; the basestation typically has available computational power. The W used at thetransmitter can be communicated to the receiver for detection.Alternatively, the receiver itself may also compute W based on its mostrecent or delayed channel estimates.

In contrast, for frequency-division duplexing (FDD) the W must becomputed at the mobile receiver (the base station receives signals fromthe mobile in a different frequency band) and communicated to the basestation via a feedback channel; consequently, quantization of W permitscomputations to be performed by searching (comparison-feedback) oversmaller sets of possible Ws. A one-shot approach compares all possiblechoices of W and then progressively signals the quantized elements of Wback to the transmitter, most significant bits first. Alternatively,partition the set of all possible W into subsets: S₁, S₂, . . . S_(K).Then at an update time t the receiver compares the choices of W in acorresponding subset S_(k(t)), and the resulting best (minimizing)choice W^((k)) from this subset is then compared to the then-currentprevious best choices W⁽¹⁾, . . . , W^((K)) from the other subsets, andthe best W^((t)) of these W⁽¹⁾, . . . , W^((k)), . . . W^((K)) is usedas the update and sent to the transmitter.

Unlike for multiple STTD encoded systems, it can be shown that choosingW to be a permutation matrix does not change the resulting channelstatistics, hence does not provide any performance advantage over anon-transformed system. For MIMO systems, W can be chosen as a unitary(complex rotation) matrix. For instance P=2, the rotation matrix is

$\begin{matrix}\begin{bmatrix}{{\cos(\theta)}\;{\mathbb{e}}^{j\;\varphi}} & {{- \sin}\;(\theta)\;{\mathbb{e}}^{j\;\varphi}} \\{\sin\;(\theta)} & {\cos\;(\theta)}\end{bmatrix} & \; & \; & {{0 \leq \theta < {\pi/2}},} & {0 \leq \varphi < {2\;\pi}}\end{matrix}$For FDD systems, the angles θ and φ can be uniformly quantized to finitenumber of values. For systems with P>2, Givens or Householder rotationscan be used.7. Asymmetric Modulation Preferred Embodiments

FIG. 3 illustrates asymmetric modulation preferred embodiments for twosymbol streams (analogous to FIG. 2 a) in which the symbol mappingdiffers for the streams; FIG. 1 d is a flow diagram. In particular, in afirst asymmetric preferred embodiment the serial-to-parallel converterprocesses 6 bits per symbol interval by alternating sets of 2 bits tothe upper symbol mapper and 4 bits to the lower symbol mapper. The uppersymbol mapper maps a set of 2 bits into a QPSK symbol, and the lowermapper maps a set of 4 bits into a 16-QAM symbol. The resulting symbolstreams (upper QPSK and lower 16-QAM) are each STTD encoded (and spread)and transmitted. In a variation, the serial-to-parallel converter couldprocess groups of 12 bits (2 symbol intervals) by 4 bits to the uppermapper for two QPSK symbols followed by 8 bits to the lower mapper fortwo 16-QAM symbols. This asymmetric symbol constellation sizes can takeadvantage of asymmetries in the channel (space diversity). The symbolmapping may be adaptive to the channel by using channel estimates tocompare capacity of the transmitter antennas. The symbol mappers mayprovide multiple symbol constellations for dynamic adaptation; or allthe symbol mappings may be performed in a single (programmable) DSP orother processor.

FIG. 4 shows a receiver for the asymmetric symbol transmission wheredetection uses the appropriate symbol constellations which are updatedintermittently (periodically).

Analogously, the asymmetric symbol preferred embodiments can also usetime diversity in that the symbol mapping may alternate in successivesymbol periods. And time diversity can be mixed with space diversity. Inparticular, for 12 bits per 2 symbol intervals the following symbolpossibilities arise:

asymmetry s₁(n) s₁(n + 1) s₂(n) s₂(n + 1) none 8PSK 8PSK 8PSK 8PSK spaceQPSK QPSK 16-QAM 16-QAM time QPSK 16-QAM QPSK 16-QAM space/time QPSK16-QAM 16-QAM QPSKFor other numbers of bits per symbol interval, other symbolconstellations would be used; for example, 18 bits per 2 symbolintervals could use 16-QAM plus 32-QAM. And the bit rate (bits persymbol interval) could vary in time, so the pairs of constellations usedwould also vary.

More generally, different combinations of 4 modulation (symbol mapping)schemes can be used, one for each transmit antenna. For multiple STTDsystems with P transmit antennas, different combinations of P modulationschemes can be used. A combination of P modulation schemes correspondsto a particular assignment of P modulation schemes to P differentsymbols.

Given a predetermined set of different modulation assignments, there area number of possible criteria for selecting the desired modulationassignment from the set. These criteria can be categorized into twogroups: fixed and adaptive. A fixed criterion does not depend on thechannel dynamics, whereas an adaptive criterion periodically updates themodulation assignment based upon the change in channel condition.

An example of fixed criteria for systems with 4 transmit antennas is toselect an asymmetric assignment of QPSK for one stream and 16-QAM forthe second stream as described above. This selection results in betterperformance compared to the symmetric assignment of 8-PSK for bothstreams. It can be argued that the aforementioned asymmetric assignmentresults in approximately 1-dB improvement over the symmetric assignmentregardless of the channel condition.

Adaptive criterion can be based on several metrics. One possible metricis to minimize the bit error rate (BER) or the frame error rate (FER)for a given channel realization while fixing the data rate. In thiscase, the set of possible modulation assignments contains differentassignments, which result in the same data rate. Another possible metricis to maximize the system throughput (data rate) for a given channelrealization while imposing a worst-case error rate (BER or FER)constraint. In this case, the set of modulation assignments containsdifferent assignments with varying data rates. In both cases, arelation/mapping between the channel parameters and the error rate (BERor FER) is needed. Such mapping depends on the type of detector that isused at the receiver. For the maximum likelihood detector, a union boundfor BER in terms of the channel parameters and modulation assignmentscheme can be derived. The selected assignment for the first case shouldbe the one that results in the minimum BER bound. For linear anditerative (zero forcing or minimum mean square error (MMSE)) detectors,the error rate is a decreasing function of minimum/worst-casepost-detection SINR, where the minimum is taken across all the Psymbols. Hence, the selected assignment for the first case should be theone that results in the largest minimum/worst-case post-detection SINR.Closed-form expressions of the post-detection SINR for each symbol canbe derived for different types of linear and iterative detectors.

Before considering the mapping between post-detection SINR and channelparameters, it is essential to discuss the operations of linear anditerative detectors. Focus on MMSE-based detectors since azero-forcing-based detector can be obtained from its MMSE analog byremoving the second term in the matrix inverse.

Repeating previously-used notation and a FIG. 3 transmitter, take thereceived signals on antenna q after down conversion (and anydispreading) as:

$\begin{matrix}{{r_{q}(n)} = {{h_{q\; 1}{x_{1}(n)}} + {h_{q\; 2}{x_{2}(n)}} + \ldots + {h_{qP}{x_{P}(n)}} + {w_{q}(n)}}} \\{= {{h_{q\; 1}{s_{1}(n)}} + {h_{q\; 2}\left( {- {s_{1}^{*}\left( {n + 1} \right)}} \right)} + \ldots + {h_{qP}\left( {- {s_{P/2}^{*}\left( {n + 1} \right)}} \right)} + {w_{q}(n)}}}\end{matrix}$and similarly

$\begin{matrix}{{r_{q}^{*}\left( {n + 1} \right)} = {{h_{q\; 1}^{*}{x_{1}^{*}\left( {n + 1} \right)}} + {h_{q\; 2}^{*}{x_{2}^{*}\left( {n + 1} \right)}} + \ldots + {h_{qP}^{*}{x_{P}^{*}\left( {n + 1} \right)}} + {w_{q}^{*}\left( {n + 1} \right)}}} \\{= {{h_{q\; 1}^{*}{s_{1}^{*}\left( {n + 1} \right)}} + {h_{q\; 2}^{*}{s_{1}(n)}} + \ldots + {h_{qP}^{*}{s_{P/2}(n)}} + {w_{q}^{*}\left( {n + 1} \right)}}}\end{matrix}$where h_(qp) is the physical channel coefficient from transmit antenna pto receive antenna q.

This can again be expressed in terms of 2-vectors and 2×2 matrices as:r _(q) =A _(q1) s ₁ +A _(q2) s ₂ + . . . +A _(qP/2) s _(P/2) +w _(q)where r_(q) is the 2-vector of components r_(q)(n), r_(q)*(n+1); S₁ isthe 2-vector of components s₁(n), s₁*(n+1); . . . , s_(P/2) is the2-vector of components s_(P/2)(n), s_(P/2)*(n+1); A_(q1) is a 2×2 matrixcorresponding to the channels of the upper pair x₁, x₂ in FIG. 3 toreceiver antenna q with first row of A_(q1) equal [h_(q1), −h_(q2)] andsecond row [h_(q2)*, h_(q1)*]; . . . , and A_(qP/2) is a 2×2 matrixcorresponding to the channels of the bottom pair x_(P-1, x) _(P) (P=4 inFIG. 3) to antenna q with first row [h_(q,P-1), −h_(qP)] and second row[h_(qP)*, h_(q,P-1)*].

As with the prior preferred embodiment, the notation can be furthercompressed with the following definitions: the 2Q×1 vector r with itsfirst two components equal the two components of r₁, next two componentsequal the two components of r₂, and so forth to the Qth last twocomponents equal to the two components of r_(Q) (i.e., verticalconcatenation of r₁, r₂, . . . , r_(Q)), P×1 vector s as the verticalconcatenation of s₁ . . . s_(P/2); and 2Q×P matrix A as the Q×P/2 arrayof 2×2 matrices A₁₁ A₁₂ . . . A_(1,P/2); A₂₁ A₂₂, . . . , A_(1,P/2) . .. ; A_(Q1), A_(Q2), . . . , A_(Q,P/2) (thus the first row of A is [h₁₁,−h₁₂, h₁₃, −h₁₄, . . . , h_(1,P-1), −h_(1P)] and second row [h₁₂*, h₁₁*,h₁₄*, h₁₃*, . . . , h_(1P)*, h_(1,P-1)*], third row [h₂₁, −h₂₂, h₂₃,−h₂₄, . . . , h_(2,P-1), −h_(2P)], fourth row [h₂₂*, h₂₁*, h₂₄*, h₂₃*, .. . , h_(2P)*, h_(2,P-1)*], and so forth down to the 2Qth row [h_(Q2)*,h_(Q1)*, h_(Q4)*, h_(Q3)*, . . . , h_(QP)*, h_(Q,P-1)*]. With thisnotation:r=A s+wThe matrix A is the 2Q×P effective transformed channel coefficientmatrix of the PQ paths: one from each of the P transmitter antennas toeach of the Q receiver antennas.

With P=4 and starting from the statistics z which is the output of thespace-time RAKE combiner:z=A ^(H) r=A ^(H)(A s+w)=C s+A ^(H) wthe LMMSE detector essentially performs a linear transformation F to thestatistics z such that the mean square error (MSE) E[∥F z−s∥²] isminimized. Again, theoretically, such linear transformation F is:F=(C+N ₀ E ⁻¹)⁻¹where N₀ is the energy of each of the 2Q components of the white noisew, E is the 4×4 diagonal matrix of symbol average energies: E₁₁ isaverage energy of s₁(n), E₂₂ average of s₁(n+1), E₃₃ average of s₂(n),E₄₄ average of s₂(n+1) (e.g., n denotes even-indexed symbol intervalsand n+1 denotes odd-indexed intervals). As noted above, the lineartransformation for linear zero-forcing (LZF) detector is simply F=C⁻¹.

The resulting minimum MSE for all the 4 symbols in s corresponds to thediagonal elements of the matrix N₀ F. The resulting linearly transformedstatistics y=Fz is essentially the soft estimate of s. Each element of yis then passed separately to a decision device (symbol detector) providethe corresponding hard symbol estimate.

For systems with 4 transmit antennas, the iterative MMSE (IMMSE)detector is a sequence of 4 linear MMSE detection stages, where eachdetection provides the soft and hard symbol estimates for each of the 4symbols in s. In each of the 4 stages, a linear MMSE transformation isperformed. After the transformation, one symbol is selected fordetection. The signal corresponding to that symbol is then regeneratedand subtracted from the received signal.

Let a₁, a₂, a₃, and a₄ denote the first, second, third, and fourthcolumns of matrix A. Also, let v(n) denote the n-th element of a vectorv. The following pseudo-code describes how IMMSE detector operates:

B = [ a₁ a₂ a₃ a₄ ] E = diag{ E₁₁ , E₂₂ , E₃₃ , E₄₄ } for p=1 to 4 F = (B^(H) B + N₀ E⁻¹ )⁻¹   : (4−p+1) × (4−p+1) matrix y = F B^(H) r        :(4−p+1) ×1 vector Find the smallest diagonal element of matrix F Selectone out of (4−p+1) symbols to be detected which corresponds to largestSINR: let that be s(o(p) ) Obtain soft estimate of symbol s(o(p) ) fromthe corresponding element of y Find the hard estimate of s(o(p) ):σ(o(p) ) r = r − a_(o(p)) σ (o(p) ) Remove column a_(o(p)) from B Removecolumn o(p) and row o(p) from matrix E endThe extension for systems with P=2p (p≧3) transmit antennas isstraightforward.

For MMSE-based detectors the post-detection symbol SINR corresponding tothe n-th element of s isSINR(n)=(E _(nn) /N ₀)F _(nn)−1where F_(nn) indicates the n-th diagonal element of matrix F. For LMMSE,matrix F is the same for all the symbols in s (see the above discussionon LMMSE). For IMMSE, matrix F is different for different symbols in ssince each symbol is detected at different iteration. This SINRexpression can be used for selecting the symbol to be detected at eachiteration. Based on the above relation, the selected symbol is the onethat results in the minimum (F_(nn)/E_(nn)). Symbol selection at eachiteration can also be thought of as finding the detection order.

The SINR expression given above is instrumental for selecting themodulation assignment (described above) as it provides an explicitrelation between the post-detection SINR (which is inversely related toBER or FER) and the channel condition (conveyed in matrix F) for bothlinear and iterative MMSE detectors. For a fixed data rate constraint,the adaptive assignment selection chooses a modulation assignment thatmaximizes the worst-case SINR (minimum SINR across all the symbols ins). For a fixed error rate constraint, the system throughput ismaximized by selecting an assignment with the highest possible data ratethat still satisfies the error rate constraint. In this case, themapping between SINR and error rate can be used.

Related to the detection ordering (symbol selection at each iteration)for an IMMSE detector, preferred embodiments also provide a bettermetric than (F_(nn)/E_(nn)). The asymmetry of the symbol constellationsimplies differing average energy for differing symbol streams. Insteadof using the post-detection symbol SINR, use the MSE scaled by theaverage symbol energy (which is: E_(nn) F_(nn)), which reflects per bitMSE. This metric works better when bit error rate is of interest ratherthan symbol error rate. The same holds for iterative zero-forcingdetector where the mean square error is equivalent to the noisevariance: using E_(nn) F_(nn) for detection ordering results in betterperformance (F=(B^(H) B)⁻¹ for iterative zero-forcing).

The symbol mapping asymmetry also extends to the case of more than 2streams with STTD encoding; that is, the transmitter of FIG. 2 c canhave an asymmetric symbol mapping among the P/2 streams.

The asymmetric modulation preferred embodiments can also follow thesetup of FIG. 2 a in that the symbol mapping may be performed prior tothe serial-to-parallel. Further, the STTD encoder outputs of theasymmetric symbols can also be linearly transformed prior totransmission; thereby combining the asymmetry with the channeladaptation of preceding preferred embodiments. In fact, a permutationlinear transformation together with fixed symbol mappers can provide thechoice among space-only, time-only, and space-time asymmetries. Thereceiver with Q antennas may be as in FIG. 2 d with the detectionincluding searches over asymmetric constellation products.

Analogous to the linear transformation preferred embodiments, for a TDDsystem both the transmitter and the receiver can compute channelconditions and thus the constellation selection, but either thetransmitter or the receiver alone could perform the computations andconvey to the other the constellation selection. In an FDD system thereceiver assesses the channel conditions and conveys information to thetransmitter; and the transmitter could perform the selection computationand convey such to the receiver.

8. Simulation Results

FIGS. 5-7 show simulation results of with and without optimalpermutation W for double STTD with P=4 transmit antennas and Q=4receiver antennas for 8-PSK, 16-QAM, and 64-QAM, respectively. Inparticular, channels A and B are flat Rayleigh fading models (peakcross-correlation of 0.6 for channel B). Here, 1234 denotes regulardouble STTD without permutation; 3124 is the optimal permutation forchannel A; and 1432 is the optimal permutation for channel B. Theoptimal permutation does not depend upon the modulation scheme, it onlydepends upon the spatial covariance profile.

FIGS. 8-9 show comparisons of both STTD encoding 8-PSK with one STTDencoding QPSK and the other 16-QAM (i.e., spatial asymmetry) for an IDchannel and for channel B, respectively. Note “ModDetect” means themodified iterative detector in which instead of using the post-detectionsymbol SINR, use the MSE scaled by the average symbol energy.

9. Modifications

The preferred embodiments can be modified in various ways whileretaining the features of linear transformation of symbols prior totransmission and/or symmetrical symbol mapping.

For example, the receiver could have the linear transformation providedby the transmitter and thereby avoid the computation; the STTD could be3×3 or larger; the asymmetric symbol encoding could also apply togeneral multiple input, multiple output (MIMO) systems; . . .

1. A method of transmitting, comprising: (a) providing a first symbolstream to a first encoder at a first time; (b) providing a second symbolstream to a second encoder at the first time; (c) encoding the firstsymbol stream to produce streams x₁, x₂; (d) encoding the second symbolstream to produce streams x₃, x₄; (e) linearly transforming the streamsx₁, x₂, x₃, x₄ by a permutation of said streams x₁, x₂, x₃, x₄ inresponse to estimated channel coefficients, wherein said permutationchanges the order of symbols in streams x₁, x₂, x₃, x₄; and (f)transmitting the linearly transformed streams x₁, x₂, x₃, x₄ to arecipient.
 2. The method of claim 1, wherein the linearly transformingof step (e) comprises selection from a finite set of lineartransformations.
 3. The method of claim 1, wherein the linearlytransforming of step (e) is responsive to parameters arising fromtransforming a channel from the recipient of the transmitting of step(f), said transforming a channel approximates an independent,identically distributed or uncorrelated channel.
 4. The method of claim1, wherein the linearly transforming of step (e) is with a P×P matrix Wdetermined by combinations of estimations of the elements of the matrix{hacek over (R)}_(TX)=W^(H)R_(TX)W.
 5. The method of claim 4, whereinthe elements of W are quantized.
 6. The method of claim 1, wherein theestimated channel coefficients are estimated with pilot symbols fromsaid recipient.
 7. The method of claim 1, wherein the first and secondsymbol streams are orthogonal frequency division multiplexing (OFDM)symbol streams.
 8. A method of transmitting, comprising: (a) providingsymbol streams s₁, s₂ to a serial-to-parallel converter and producingsymbol stream s₁, s₂ in parallel; (b) providing symbol stream s₁ to afirst space-time transmit diversity encoder at a first time; (c)providing space-time transmit diversity encoded stream s_(1,1), s_(1,2),−s_(1,2)*, s_(1,1)* from said first space-time transmit diversityencoder; (d) providing symbol stream s₂ to a second space-time transmitdiversity encoder at the first time; (e) providing space-time transmitdiversity encoded stream s_(2,3), s_(2,4), −s_(2,4)*, s_(2,3)* from saidsecond space-time transmit diversity encoder, wherein said stream s₂ isdifferent from said stream s₁; (f) linearly transforming said s_(1,1),s_(1,2), −s_(1,2)*, s_(1,1)* and s_(2,3), s_(2,4), −s_(2,4)*, s_(2,3)*by a permutation of said s_(1,1), s_(1,2), −s_(1,2)*, s_(1,1)* ands_(2,3), s_(2,4), −s_(2,4)*, s_(2,3)* in response to estimated channelcoefficients, wherein said permutation changes the order of symbols instreams s_(1,1), s_(1,2), −s_(1,2)*, s_(1,1)* and s_(2,3), s_(2,4),−s_(2,4)*, s_(2,3)*; and (g) transmitting said linearly transformeds_(1,1), s_(1,2), −s_(1,2)*, s_(1,1)* and s_(2,3), s_(2,4), −s_(2,4)*,s_(2,3)*.
 9. The method of claim 8, wherein said linearly transformingstep (f) is selection from a finite set of linear transformations. 10.The method of claim 8, wherein said symbol streams s_(1,1), s_(1,2),−s_(1,2)*, s_(1,1)* and s_(2,3), s_(2,4), −s_(2,4)*, s_(2,3)* areorthogonal frequency division multiplexing (OFDM) symbol streams. 11.The method of claim 8, wherein said linearly transforming step (f) is aweighted permutation of said s_(1,1), s_(1,2), −s_(1,2)*, s_(1,1)* ands_(2,3), s_(2,4), −s_(2,4)*, s_(2,3)*.
 12. The method of claim 8,wherein said linearly transforming step (f) is with parameters providedby a recipient of said transmitting of step (g) of claim
 8. 13. Themethod of claim 12, wherein said recipient provides said parameters viaa feedback channel.
 14. The method of claim 8, wherein said linearlytransforming step (f) is with parameters derived from receipt of signalsfrom a recipient of said transmitting of step (g) of claim
 8. 15. Themethod of claim 14, comprising transmitting said parameters to saidrecipient via a signaling channel.
 16. The method of claim 8, whereinsaid linearly transforming step (f) is with parameters arising fromtransforming a channel from a recipient of said transmitting of step (g)of claim 8, said transforming a channel approximates an independent,identically distributed or uncorrelated channel.